Age Calibration

which relates the TIR-to-FUV flux ratio, y = log(F_TIR/F_FUV), also referred to as the infrared-excess (IRX). This expression, and the TIR-to-FUV flux ratio, appear to be much a more robust and universal tracer of dust extinction than other methods. As a quantitative dust estimator, it is found to be almost independent of dust and stellar geometry, provided that the galaxies are forming stars actively (Buat & Xu 1996; Buat et al. 1999; Gordon et al. 2000). With no available Hβ data, the A(Hα) extinction was calculated using the relationAF U V = 1.4A(Hα)of Boissieret al. (2005). This equation assumes the extinction curve of Pei (1992) and that the colour excess of the stellar continuum (E(B−V)_S) relative to the gaseous emission (E(B−V)_g) isA_{F U V} = 8.87E(B−V)_S (Calzetti 1994, 1997).

Figure 4.2: The effect of varying SFH, IMF, and metallicity on model Hα to FUV flux ratios, log(FHα/FF U V). Upper left: Flux ratio in the case of both instantaneous (dashed lines) and continuous SFHs (solid lines). The models in this panel assume a Salpeter IMF and range of metallicities: Z =0.02 (red circles), 0.04 (blue squares), 0.008 (green diamonds) and 0.004 (black triangles). The underlying histogram shows the range of measured flux ratios for each galaxy in the sample. Upper right: Model Hα to FUV flux ratios as a function of varying IMF: (A) Salpeter,α= 2.35andM_up= 100M; (B) truncated Salpeter,α= 2.35 and Mup = 30M; (C) and Miller-Scalo, α = 3.3 and Mup = 100M. In these cases, the assumed SF law is instantaneous and the metallicities are the same as those in the upper left panel, and with the same colour coding. Bottom left: A comparison between an instantaneous SFH with recent 25 Myr-old burst (dashed lines) to a plain instantaneous burst (solid lines). The latter are the same solid curves as shown in the upper left and the same metallicities (and their colours) have been used. Bottom right: A comparison of the systematic model uncertainties with random uncertainty in the flux measurements. The instantaneous and (instantaneous+recent burst) models are shown (solid and dashed red lines, respectively). Photometric measurement errors for the galaxies (in three groups) are indicated by the horizontal bars.

log(LHα) = log(EW(Hα)) +log(C(Hα)) (4.4)

L_{F U V} =

RF(λ)S(λ)dλ R F(λ)dλ =

P₁₈₀₉

λ=1341F(λ)S(λ) P1809

λ=1341F(λ) (4.5)

where EW(Hα) is the Hα equivalent width (in ˚A), andC(Hα) is the Hα continuum (measured as the median continuum luminosities at wavelengths 6550 and 6590 ˚A). The F(λ)term in Eqn. 4.5 is the GALEX response curve andS(λ)is the luminosity of the SED in units of ergs⁻¹ ˚A⁻¹.

To assess the suitability and robustness of our reference model we calculated the effect of changing various model inputs on the SB99 FHα/FF U V ratios (Figure 5.3). The upper left panel shows of Fig. 5.3 shows the ratios for both an instantaneous and continuous SFH, and shows the former to be much better match to the observed ratios. Like Iglesias-P´aramo et al. (2004), we find an instantaneous SFH to be a more sensitive discriminant of the age variations in younger star forming regions. One might naively assume that because our galaxies are not starbursts they would be better modeled assuming continuous star formation. However, as our pixel approach delineates individual star forming regions (as opposed to integrating the total star formation across the face of the galaxy), each particular star-forming region, represented by a pixel in the image, is more accurately regarded as having undergone a stellar burst. Although the SFHs of individual regions will be more complex, an instantaneous starburst is a reasonable approximation for localised regions of star formation younger than10⁸ yr (e.g., Pasquali et al. 2008).

In the upper right panel of Fig. 5.3 we show the effect that changing the IMF has on the Hα-to-UV ratio for a range of metallicities. All three cases of IMF are shown (A, B, and C) which represent a plausible spread of slopes and mass cut-offs. For each case we apply metallicities ofZ = 0.02 (solar), 0.04, 0.004, and 0.008. We see that for fixed metallicity, the variation between the different IMFs is no more than 0.4 dex for the youngest ages, reducing to ∼0.1 dex beyond ∼6 Myr. Alternatively, for a given fixed IMF, the variation in Hα-to-UV with metallicity is at most∼0.5dex over the longest ages, reducing to∼0.2 dex within the first few Myr.

We would expect that the Hα-to-UV ratios are especially sensitive to SFHs that containing a recent burst of star formation (say 25 Myr). These would no longer emit in Hα but still carry some output in the FUV given the relatively longer ages of the lower mass UV-emitting stars. To investigate this, we compute FUV* which is the FUV flux generated from a current burst of star formation combined with a 25 Myr-old burst with identical SFR. In the lower left panel of Fig. 5.3 we compare the flux ratio F_Hα/F_{F U V}∗

(for a SFH with an additional burst) to the same ratios FHα/FF U V plotted in the upper left (for an instantaneous SFH). The figure shows that there is negligible difference (<0.15 dex) between either case of SFH, for a fixed given metallicity. We therefore conclude that recent bursts are much less of an effect on the FUV than one might expect.

The lower right panel of Fig. 5.3 puts the size of this variation due to SFH into the context of the measurement errors. The red solid and dashed lines show the reference model for both the instantaneous and (instantaneous+recent burst) cases. Also shown at each point are the1σ measurement uncertainties for all of the galaxies. We see that compared to the observational errors, systematic uncertainty due to the SFH is negligibly small.

We conclude that of all the model inputs, it is choice of IMF that matters most over the first few Myr after an instantaneous burst of star formation. Metallicity matters more after several Myr have elapsed, and in both cases the range is 0.4 to 0.5 dex at most, and is comparable with the observation errors. We also conclude that a continuous SFH can be ruled out on the basis of our observed F_Hα/F_{F U V} ratios, and that an instantaneous burst gives a more realistic distribution of values. While one might expect that the addition of a recent burst of (25 Myr ago) would affect the FUV flux significantly, we find that this is not the case. Most important of all, we see that while the change in Hα-to-UV fluxes in absolute terms is about 0.4 to 0.5 dex due to changing model inputs, the change in relative terms (i.e. difference from 1 to 10 Myr) is much less (<0.15dex). Therefore, any relative age comparisons are largely immune to the choice of model inputs.